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Here's the full and uncut version of our interview with Fields Medallist Cédric Villani. We'll publish a slightly more polished version when we get the time, with more explanations, but thought you'd like the chance to listen to the whole thing.

By cleverly cross-referencing different databases it can be possible for evil adversaries to reveal intimate information about individuals. Given that it's hard these days to keep your details off these databases, what can be done to protect privacy? We talk to Cynthia Dwork from Microsoft, whose talk at the ICM showcases some mathematical tools to keep our details safe.

We're at the massive conference dinner, talking to Alex Bellos, author of best-selling popular maths book Alex's adventures in numberland, mathematician Colva Roney-Dougal, other delegates and ourselves.

New treatments and drugs are tested extensively before they come on the market using randomised controlled trials (RCTs). We talk to David Spiegelhalter (Winton Professor of the Public Understanding of Risk), Sheila Bird (Professor at the Medical Research Council Biostatistics Unit), and Nigel Hawkes (journalist and director of Straight Statistics).

Vaccination is an emotive business. The furore around the MMR vaccine and autism has shown that vaccination health scares can cause considerable damage: stop vaccinating, and epidemics are sure to follow. But how do scientists decide whether a vaccine and a vaccination strategy are effective and safe? We talk to Paddy Farrington, Professor of statistics at the Open University. You can also read the accompanying article.

In our fourth online poll to find out what you would most like to know about our Universe, you told us that you would like to know how gravity works. We took the question to Bangalore Sathyaprakash from the University of Cardiff, and here is his answer. You can also read the accompanying article.